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You are not logged in. #76 20130418 00:35:52
Re: Julianthemath's number 3That is very good, you kept the dominant terms. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #77 20130418 00:44:51
Re: Julianthemath's number 3Exactly. They seem to do the job good enough. I will try getting the closed form analitically today. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #78 20130418 00:51:43
Re: Julianthemath's number 3Uh wait. That is the analytical answer up there. So you will looking for a shorter one? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #79 20130418 00:53:59
Re: Julianthemath's number 3You didn't get it by analityc methods. You used M's FindSequenceFunction command. I want to see if I can get the answer analitically. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #80 20130418 00:59:26
Re: Julianthemath's number 3All you provided me was with your original algorithm. I had to use the sequence. And why not just try induction and prove the a_n is correct? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #81 20130418 01:11:39
Re: Julianthemath's number 3Do you think there is a nicer reccurence for the sequence? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #82 20130418 01:13:50
Re: Julianthemath's number 3Maybe. The weirdest thing is that sequences can have more than one difference equation. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #83 20130418 01:54:36
Re: Julianthemath's number 3I have the difference equation. It's a[n+4]4a[n+2]a[n]+4a[n2]=0. Don't ask how I got it! Last edited by anonimnystefy (20130418 02:41:07) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #84 20130418 01:56:00
Re: Julianthemath's number 3I am going to ask just that. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #85 20130418 01:57:42
Re: Julianthemath's number 3It is a bit tough to explain. I played a little bit of spotthepattern... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #86 20130418 01:59:41
Re: Julianthemath's number 3The solution to that will probably be longer than the other one. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #87 20130418 02:01:24
Re: Julianthemath's number 3I think you will get the same solution. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #88 20130418 02:04:20
Re: Julianthemath's number 3Possibly, or the trigonometric terms will be replaced by (1)^n or something like that. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #89 20130418 02:13:04
Re: Julianthemath's number 3The trigonometric terms will be replaced by i^n and (i)^n. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #90 20130418 02:16:56
Re: Julianthemath's number 3Yes, that is possible too but I would not exactly call that simpler. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #91 20130418 02:26:28
Re: Julianthemath's number 3True. But the reduced form looks really nice, though! The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #92 20130418 02:28:04
Re: Julianthemath's number 3It is an asymptotic form yes? It is supposed to be shorter and easier to compute. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #93 20130418 02:29:53
Re: Julianthemath's number 3Yes. It looks much much prettier than the nasty exact one. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #94 20130418 02:33:02
Re: Julianthemath's number 3But you possibly missed the forest for the trees. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #95 20130418 02:41:46
Re: Julianthemath's number 3How? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #96 20130418 02:44:19
Re: Julianthemath's number 3It appears there might be a pattern worth investigating that is much simpler. It may not hold but it is worth a look. You have to get out of the box axiomatic math puts you in. It is small, dark and has little air. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #97 20130418 02:47:50
Re: Julianthemath's number 3Which pattern? In the binary representation? That is the one I used to get the difference equation. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #98 20130418 02:50:51
Re: Julianthemath's number 3One question at a time can be investigated well. This one is more important.
No, not that one. Look below, is there anything cooking? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #99 20130418 02:56:39
Re: Julianthemath's number 3Well, they approach 1. That is why my formula is an asymptotic one. I also notice that every fourth term repeats two terms later. I do not notice anything else. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #100 20130418 03:04:20
Re: Julianthemath's number 3Yes, the differences between the asymptotic form and the actual answer follow a pattern. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 